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2 years ago

How many ways can we pick three distinct integers from {1, 2, ..., 15} such that their sum is divisible by 3?

Mathematics

1 answer:

gogolik [260]2 years ago

5 0

Answer:

Clearly from 1 to 15 we can only have the sum 6,9,12 and 15 to be divisible by 3.

Now meaning we have 4! ( 4 factorial) which implies 4x3x2x1= 24 .

We have 24 ways to pick distinct integers that are divisible by 3.

Step-by-step explanation:

The first thing you need to do is to look for numbers that are divisible by 3. Then you take its factorial

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2(35) - 1/2(15)
or 70 - 7.5

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2 years ago

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2 years ago

Suppose on a certain planet that a rare substance known as Raritanium can be found in some of the rocks. A raritanium-detector i

Andrews [41]

Answer:

the probability the rock has raritanium is 0.9670

Step-by-step explanation:

These events have been defined as

Z: sample has raritanium

Y: the reading from detector is positive

Z': sample has no raritanium

Y': Reading from detector is negative

P(z) = 0.13

P(y'/z) = 0.02

P(y/z')= 0.005

We need to find p(z/y)

= p(z/y) = p(z ∩ y)/p(y)

= P(z) - p(z∩y)/0.13 = 0.02

Remember the value of p(z) = 0.13

So when we cross multiply we get

0.13 - p(z ∩ y) = 0.02 x 0.13

0.13 - p(z ∩ y) = 0.0026

-p(z ∩ y) = 0.0026 - 0.13

Such that

p(z ∩ y) = 0.1274

P(y/z')= 0.005

P(z∩y') = 0.005

Since p(z) = 0.13

P(z') = 1-0.13

P(y) - p(z∩y)/0.87 = 0.005

We cross multiply

P(y) - 0.1274 = 0.005x0.87

P(y) = 0.1274+0.00435

P(y) = 0.13175

We have 0.1274/0.13175

= 0.9670

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6 0

2 years ago

. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ft/sec, and the bottom of the l

Vlada [557]

Answer:

0.75 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.

So we can set a Pythagoras theorem as:

$x^2+y^2=25^2$

$x^2+y^2=625$

Now, we need to find the derivative of above equation with respect to time.

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: $20-1(5)=20-5=15$

Let us solve for y using Pythagoras theorem.

$y^2+15^2=25^2$

$y^2+225=625$

$y^2=625-225$

$y^2=400$

Take positive square root:

$\sqrt{y^2}=\sqrt{400}$

$y=20$

Upon substituting our given values in derivative equation, we will get:

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

$2(15)\cdot(-1)+2(20)\cdot \frac{dy}{dt}=0$

$-30+40\cdot \frac{dy}{dt}=0$

$40\cdot \frac{dy}{dt}=30$

$\frac{dy}{dt}=\frac{30}{40}$

$\frac{dy}{dt}=0.75$

Therefore, the ladder is moving up at a rate of 0.75 feet per second.

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2 years ago

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tia_tia [17]

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Step-by-step explanation:

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2 years ago

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